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Optical field enhancement comparison between long-range surface plasma waves, and waves induced by resonant cavity
Volume
5 6, number
3
OPTICS COMMUNICATIONS
1 December
1985
OPTICAL FIELD ENHANCEMENT COMPARISON BETWEEN LONG-RANGE SURFACE PLASMA WAVES, AND WAVES INDUCED BY RESONANT CAVITY Y. Ll?VY, Y. ZHANG
’ and J.C. LOULERGUE
Institut d’optique ThPorrque et Appliqutke, lJnruersit6de Paris-Sud, Centre d’orsay, 91405 Orsay Ckdex, France Received
26 July 1985
We present a comparison between the enhancement of the optical fields obtainable by two different prism-coupling geometries: the long range surface plasmons and a dielectric stratified medium or resonant cavity. The analysis shows that the resonant cavity can give rise to a field enhancement larger than the other geometry, with the advantage of being without damage to the structure because of dissipation of power in the metal.
1. Introduction The presence of a large electric field in a material gives rise to several measurable nonlinear effects, such as second harmonic generation, four wave mixing, quadratic Kerr effects and power dependent refractive index phenomena. These effects are usually observed by irradiating the nonlinear material by one or more focused laser beams. The presence of a surface breaks the inversion symmetry of a medium normal to the boundary and makes second order nonlinear interaction possible [ 11. In recent years the generation of second harmonic radiation at metal surfaces has been studied extensively, because the intensity of the produced harmonic can be increased by over an order of magnitude by use of the enhanced fields at the metal boundaries associated with surface plasmons [2-61. Until now the theoretical and experimental investigations of second harmonic generation at metal surfaces have been based on either a Kretschmann or an Otto geometry. More recently, a modified Kretschmann (or Sarid) geometry has been proposed [7-91, to increaSe the reflected second-harmonic radiation produced at the surface of a nonlinear medium, by roughly two orders of magnitude. However, the fields ’ Visiting
Scholar from Tianjin University, Precision Instruments Engineering, Tianjin,
Department China.
of
0 030-4018/85/$03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
being concentrated in the evanescent tails in the media bounding the metal, damage the film because of dissipation of power in the metal by the fundamental fields is foreseen as a problem, even if the metal thickness is very small [9,10]. However, there is an optimum non-absorbing geometry for which the average spot size and interaction length yield maximum performance: by using the total reflection of a plane wave on a dielectric stratified medium of particular configuration, which provides a very high energy density by means of leaky waves. Although optical waveguides have many advantages to probe and characterize nonlinear films and surfaces [ 11 ,121, they have never been used to obtain a nonlinear phenomena on a surface or in a thin film. By using guided wave optics one is freed from the restriction of a finite focal depth, and the interaction length is only limited to absorption or scattering in the waveguide. We are going to present here a comparison between the properties of longrange surface plasma waves and waves induced by a resonant cavity!
2. Outline of theory It has recently been shown that the excitation of long range surface plasmon polaritons provide very strong nonlinear interactions [8,9]. These modes are 155
Volume 56, number 3
OPTICS COMMUNICATIONS
Metal Film
TM wave
1 December 1985
Dielectric layer
TM or TE wave
Fig. 1. The prism-coupling geometry for exciting the longrange surface plasma wave. n3 is the thin metallic film surrounded by two adjacent equal dielectric media a;12and Q.
Fig. 2. The prism
guided by a thin metal layer about 150 A of thickness, surrounded by two adjacent dielectric media of almost equal refractive indices. Surface plasmon waves having an anti-symmetric transverse field distribution can propagate over long distances. The geometry consists of a metal film a3 with a substrate &&ton one side and thin dielectric layer !$ on the other side (fig. 1). Light is coupled through the thin dielectric layer from a high index prism s1,. For an optimal choice of metal film and dielectric layer thicknesses, the angular width of the ATR resonance can be reduced by roughly one order of magnitude and the electromagnetic field at the surface of the metal film can be increased by one or two orders of magnitude. The field enhancement and the angular width of the reflectivity minimum are strongly dependent on the metal film thickness. The efficiency of the coupling is best with an optimal thickness of the dielectric gap. These modes are different from the short range surface plasmons usually obtained from thicker metal films. Field enhancements can also be obtained from resonant cavity excitation [ 1 I] and the geometry is quite similar to the previous one. It means that the metal film is now replaced by a thin dielectric layer whose refractive index is higher than those of the surrounding media (fig. 2). Without the coupling prism, the layer can be considered as a waveguide having different guided propagation modes, for the two states of polarisation TE and TM. We recall that plasmon polaritons can be only excited with TM polarisation. Depending on the thickness of the waveguide film, separate modes TE and TM propagate freely inside
the structure. The incident beam issued from the prism is totally reflected by the multilayered structure and the reflectivity is equal to unity. Let us consider the case represented in fig. 2. The configuration involves four dielectric, homogeneous, isotropic, non absorbing media, two of which are thin films. The subscripts 1, 4 refer to the prism, gap, layer, resonant layer and the outside medium. The optical constants of the media (thickness dj, refractive index ni) are choosen as to give inhomogeneous fields in CZz and S& and homogeneous fields in C13. These conditions are easily obtained if the incidence angle 0 in the prism is smaller than the critical angle between !Cl, and .Q3 and larger than this one between a, and fi2, Qt. These conditions imply that the transmitted wave in !&t is evanescent and the field in a3 results from the superposition of two plane incident and reflected waves with amplitudes equal to A 3 and B3 respectively. It has been shown [ 121 that the field inside the resonant cavity is maximum, if the transverse resonance condition is satisfied by:
156
2Bd3 - $31 ~ +34 = 2mn,
(1)
where m is an integer which identifies the mode number. With k,, = w/c; B2 = kie3 - f12; G34 is the phase shift undergone by the incident wave A3 on the boundary Q31R,; $31 is the phase shift undergone by the B3 wave which is partially reflected on the C13/R,/a2, interface taking into account the presence of the prism. In this relation, /3 is the longitudinal propagation constant. The influence of the polarisa-
Volume 56, number 3
OPTICS COMMUNICATIONS
1 December 1985
tion TE or TM is involved through the phase shifts
A, B, C, are complex A’, A”, B’, B”, C’, C” are the
$31 and $34. For the TM case, tan $34 = e3C/qB and for d, > h = e3A/eZB, where and J/31= $32 with tan($32/2)
real and imaginary parts, respectively. When the metal film is thick enough. two surface plasma waves propagate on each surface of the film. If the thickness decreases the fields of these two surfaces waves overlap inside the metal layer and a long range and a short range plasma surface wave can be excited simultaneously with different propagation constants /3. The pairs of real and imaginary parts of fl are characteristic of the short range and long range surface plasma waves.
A2=fi2-k;e2,
C2=f12-k;e4.
(2)
The field in the resonant cavity is given by: U~(X, z) = exp(-jf3x)
[A3 exp(-jBz)
+B3exp(+jBz)]
, (3)
As, B3 are the amplitude
of the incident and reflected waves in a,. U3 = Ey in the TE case and U, = Hu in the TM case. The calculationofthe squared field U3 at the Q3/a4 interface normalised to the squared field U, in the prism is given by a=P[l-
Ir311 lr34lexp(-j 2Bd3 - G31 - J/34)1--2, (44 of the thickness d,,
where P is a quantity independent and r31 and r34 are the Fresnel reflection coefficients at the LI3/Q2,/Ql and !&/fi4 interfaces. As the transverse resonance condition is satisfied, the normalised field intensity is maximal and is given by s = B(1 - Ii-31 l)p
,
(4b)
where lr31 1is not equal to unity and depends on the thickness of the gap, and lr34 I = 1 as the a3 and s1, media are non absorbing. Due to the fact that lrN[ can be close to unity, the intensity can reach a high value. In the case oflong range plasmon polaritons, eqs. (1) can be used to give the dispersion relation of resonant TM modesguided by a thin metallic film surrounded by two adjacent dielectric media of almost equal refractive index. It has been shown [ 131 that a simplification of eq. (1) can be performed and provides the two following relations with real quantities: tan [(B’/B”) In lk I] + k”/k’ = 0 ,
(54
IklI2KB” ,
(5b)
d3 = -In
with k=(k34
-j)(Q-j)l(k34+j)(k32
k34 = tan(J/&),
k32 = tant$&)
+j), .
In eqs. (2), /3 is a complex variable: /3 = /3’ t j/I” where 0’ is related to the mode phase velocity and 0” is the mode attenuation coefficient. Only the mode m = 0 is considered. Note also that all the parameters
3. Results The following discussion is devoted to making a comparison of the field enhancements between the long range plasmas wave method and the resonant cavity excitation. We wish to show theoretically the magnitude of the field enhancements for both geometries discussed above. To demonstrate the field enhancement obtainable with both configurations (fig. 1, fig. 2), we choose parameters appropriate to the case of a silver metal film having dielectric constant e& = ~3 = -16 +j 0.52 at a wavelength of 632.8 nm bounded by two dielectric media of equal refractive index e2 = e4 = 2.25. For the resonant cavity configuration, we choose a high dielectric constant film a3 = 5.29 surrounded by the dielectric media e2 = e4 = 2.25. For both configurations, the incident light is coupled to the film through a high refractive index prism n 1 = 1.94325 or el = rzf = 3.78. The field enhancement can be only calculated with TM polarized light for the metal structure and with both TE and TM modes in the resonant dielectric structure. Fig. 3 shows the reflectivity curve as function of the incident angle inside the prism for dAg = 200 A and d,, = 9500 a and the angular width of the resonance close to 0.05”. The ratio u of the absolute square of the magnetic field inside the structure and the prism as function of z is shown in fig. 4 for three different incident angles: (a) 0 = 51.41” the resonant angle, (b) and (c) the angles corresponding to the half width of the resonance curve (fig. 3). The ratio is roughly divided by two. As the metal thickness decreases, the angular width of the resonance can be reduced by over an order of magni157
Volume
56. number
OPTICS COMMUNICATIONS
3
1 December
1985
‘base ;hift
0.
e 58. 91.30
51.40
SO
60.00
60. n1
91.50
Fig. 3. Reflectivity as a function of the incident angle 0 (degrees) for a long-range plasma wave geometry. The resonance angle occurs at 51.41” with eAg = -16 + j0.52, ~2 = ~4 = 2.25, E, = 3.78, and d& = 2008. Note the resonance width is close to 0.05”) corresponding to the 5 1.39” and 5 1.44” offresonance angles.
tude and the field enhancement can be higher. In this case, the system is limited by the diffraction effects associated with the finite width of the laser beam and by the angular aperture of the beam. These results have to be compared with the following curves in figs. 5,6,7,8. We calculated two config-
Fig. 5. Phase shift of the reflected beam as plotted as a function of the incidence angles e (degrees). The resonance angle occurs at 60” for TM polarized light with, er = 3.78, e2, ~4 = 2.25, es = 5.39, and d2 = 4000 A, d3 = 1095 A. The phase shift origin is arbitrary. The resonance width is close to 0.05“.
urations with the finite width of the laser beam and by the angular aperture of the beam. These results have to be compared with the following curves in figs. 5, 6, 7,8. We calculated two configurations with the dielectric resonant film; the first one is appropriate to the TM mode, (figs. 5,7), and the last to the TE mode (figs. 6,8). The thicknesses
lr
Phase shift
T-
a 0
100
200
e 76.
IO
76.20
3on
Fig. 4. Ratio o corresponding to the absolute square of the magnetic field IH~]~ inside the structure, divided by the incident magnetic field lHY I* in the prism as function of z. The curves given on the fire are calculated for the plasma resonance angles (a) and off-resonance (b and c). (a) 0 = 5 1.4 1”) (b) e = 51.39’;(c) e = 51.44”.
1.58
OI. IDO
Fig. 6. Phase shift of the reflected beam inside the prism as function of the incidence angle 0 (degrees). The resonance angle is at 76.12” for a TE polarized light. The gap and cavity thicknesses are respectively equal to 3000 A and 1095 A. The media are er = 3.78, ea = 2.25, es = 5.39, ~4 = 2.25. The phase shift origin is arbitrary. The resonance width is close to 0.05”.
OPTICS COMMUNICATIONS
Volume 56, number 3
0
400
BOO
1200
1 El00
Fig. 7. The ratio o (corresponding to the normalised IH,, 1’ for a TM polarized light) inside the resonant dielectric structure for the same parameters as given in fig. 5. The curves a, b, c, given on the figure are calculated for the incidence angles at resonance (60’) and off resonance (59.97” and 60.03”). The two curves corresponding to the off resonance angles are superposed.
of the gap layer and resonant cavity are equal to 4000 A and 1095 A for the TM mode; the maximum field enhancement occurs at the incidence angle of 60”. For the other confguration, the thicknesses are equal respectively to 3000 A and 1095 A for the TE mode.
1 December 1985
The maximum field enhancement is obtained for an incidence angle of 76” 12. In both cases, we considered only the m = 0 guided mode of the cavity. Around the resonance angle, the phase shift of the reflected beam undergoes a strong modification as shown in figs. 5,6. The slopes of the curves at 60’ and 76.12’ depend on the thickness of the gap. The angular resonance widths are evaluated from the linear part of the curve and are close to 0.05”. The choice of the gap thicknesses (3000 A and 4000 8, for TE and TM modes respectively) has been made to have the angular resonance width as in the case of the metal structure described above. Therefore, we can compare the field enhancements provided from these different configurations, with the same experimental conditions. Figs. 7 and 8 show the ratio u of the absolute squared IU12 inside the structure and in the prism versus z. We recall that U = HY (fig. 7) or U = Er (fig. 8) in TM or TE mode. If we compare the field enhancement, illustrated in fig. 4 for the metal film structure and fig. 7 for the resonant dielectric cavity. we note that the field intensity is roughly six times stronger in the dielectric structure as compared to the metal film (note the scale relative to the ratio u).
4. Conclusion We have compared the enhanced fields associated with the long range surface plasmon resonance and with the resonant cavity structure. We found that for the same angular width of the resonance, the dielectric structure can produce an enhancement six times higher than from the long range surface plasmons. Furthermore, the problem of dissipation of power in the metal which constitutes a thermal parasite effect can be avoided by the dielectric structure.
i0
0
Acknowledgement 1000
15110
2000
Fig. 8. The ratio e (corresponding to the normalised @I” for a TE polarized light) inside the multilayered dielectric structure for the same parameters asgiven in fig. 6. The curves a, b, c, given on the figure are calculated for the incident angles at resonance (76.12’) and off resonance (76.09” and 76.14”).
The authors would like to thank J.D. Swalen from the IBM Research Laboratory, San Jose, California, for helpful discussions concerning the field enhancements.
159
Volume 56, number 3
OPTICS COMMUNICATIONS
References [ 1) N. Bloembergen and P.S. Pershan, Phys. Rev. 128 (1962) 606. [2] H.J. Simon, D.E. Mitchell and J.G. Watson, Phys. Rev, Lett. 33 (1974) 1531. [ 31 H J. Simon, R.E. Bemier and J.G. Rako, Optics Comm. 23 (1977) 245. [4] C.K. Chen, A.R.B. de Castro and Y.R. Shen, Optics Lett. 4 (1979) 393. [5] F. de Martini, M. Colocci, S.E. Kohn and Y.R. Shen, Phys. Rev. Lett. 38 (1977) 1223. [6] C.K. Chen, A.R.B. de Castro, Y.R. Shen and F. de Martini, Phys. Rev. Lett. 43 (1979) 946.
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1 December 1985
[7] D. Sarid, Phys. Rev. Lett. 47 (1981) 1927. [ 81 R. Moshrefzadeh, R. Fortenberry, C. Karaguleff and G.I. Stegeman, N.E. Van Wijck, W.M. Hetherington III, Optics Comm. 46 (1983) 257. [9] R.T. Deck and D. Sarid, J. Opt.Soc.Am. 72(1982) 1613. [ 101 G.I. Stegeman, J J. Burke and D.G. Ha.& Appl. Phys. Lett. 41 (1982) 906. [ll] Y. Levy,Can. J.Phys. 58 (1980) 1525. [ 121 P.K. Tien and R. Ulrich, J. Opt. Sot. Am. 60 (1970) 1325. [ 131 D. Sarid, R.T. Deck and J J. Fasano, J. Opt. Sot. Am. 72(1982) 1345.
5 6, number
3
OPTICS COMMUNICATIONS
1 December
1985
OPTICAL FIELD ENHANCEMENT COMPARISON BETWEEN LONG-RANGE SURFACE PLASMA WAVES, AND WAVES INDUCED BY RESONANT CAVITY Y. Ll?VY, Y. ZHANG
’ and J.C. LOULERGUE
Institut d’optique ThPorrque et Appliqutke, lJnruersit6de Paris-Sud, Centre d’orsay, 91405 Orsay Ckdex, France Received
26 July 1985
We present a comparison between the enhancement of the optical fields obtainable by two different prism-coupling geometries: the long range surface plasmons and a dielectric stratified medium or resonant cavity. The analysis shows that the resonant cavity can give rise to a field enhancement larger than the other geometry, with the advantage of being without damage to the structure because of dissipation of power in the metal.
1. Introduction The presence of a large electric field in a material gives rise to several measurable nonlinear effects, such as second harmonic generation, four wave mixing, quadratic Kerr effects and power dependent refractive index phenomena. These effects are usually observed by irradiating the nonlinear material by one or more focused laser beams. The presence of a surface breaks the inversion symmetry of a medium normal to the boundary and makes second order nonlinear interaction possible [ 11. In recent years the generation of second harmonic radiation at metal surfaces has been studied extensively, because the intensity of the produced harmonic can be increased by over an order of magnitude by use of the enhanced fields at the metal boundaries associated with surface plasmons [2-61. Until now the theoretical and experimental investigations of second harmonic generation at metal surfaces have been based on either a Kretschmann or an Otto geometry. More recently, a modified Kretschmann (or Sarid) geometry has been proposed [7-91, to increaSe the reflected second-harmonic radiation produced at the surface of a nonlinear medium, by roughly two orders of magnitude. However, the fields ’ Visiting
Scholar from Tianjin University, Precision Instruments Engineering, Tianjin,
Department China.
of
0 030-4018/85/$03.30 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
being concentrated in the evanescent tails in the media bounding the metal, damage the film because of dissipation of power in the metal by the fundamental fields is foreseen as a problem, even if the metal thickness is very small [9,10]. However, there is an optimum non-absorbing geometry for which the average spot size and interaction length yield maximum performance: by using the total reflection of a plane wave on a dielectric stratified medium of particular configuration, which provides a very high energy density by means of leaky waves. Although optical waveguides have many advantages to probe and characterize nonlinear films and surfaces [ 11 ,121, they have never been used to obtain a nonlinear phenomena on a surface or in a thin film. By using guided wave optics one is freed from the restriction of a finite focal depth, and the interaction length is only limited to absorption or scattering in the waveguide. We are going to present here a comparison between the properties of longrange surface plasma waves and waves induced by a resonant cavity!
2. Outline of theory It has recently been shown that the excitation of long range surface plasmon polaritons provide very strong nonlinear interactions [8,9]. These modes are 155
Volume 56, number 3
OPTICS COMMUNICATIONS
Metal Film
TM wave
1 December 1985
Dielectric layer
TM or TE wave
Fig. 1. The prism-coupling geometry for exciting the longrange surface plasma wave. n3 is the thin metallic film surrounded by two adjacent equal dielectric media a;12and Q.
Fig. 2. The prism
guided by a thin metal layer about 150 A of thickness, surrounded by two adjacent dielectric media of almost equal refractive indices. Surface plasmon waves having an anti-symmetric transverse field distribution can propagate over long distances. The geometry consists of a metal film a3 with a substrate &&ton one side and thin dielectric layer !$ on the other side (fig. 1). Light is coupled through the thin dielectric layer from a high index prism s1,. For an optimal choice of metal film and dielectric layer thicknesses, the angular width of the ATR resonance can be reduced by roughly one order of magnitude and the electromagnetic field at the surface of the metal film can be increased by one or two orders of magnitude. The field enhancement and the angular width of the reflectivity minimum are strongly dependent on the metal film thickness. The efficiency of the coupling is best with an optimal thickness of the dielectric gap. These modes are different from the short range surface plasmons usually obtained from thicker metal films. Field enhancements can also be obtained from resonant cavity excitation [ 1 I] and the geometry is quite similar to the previous one. It means that the metal film is now replaced by a thin dielectric layer whose refractive index is higher than those of the surrounding media (fig. 2). Without the coupling prism, the layer can be considered as a waveguide having different guided propagation modes, for the two states of polarisation TE and TM. We recall that plasmon polaritons can be only excited with TM polarisation. Depending on the thickness of the waveguide film, separate modes TE and TM propagate freely inside
the structure. The incident beam issued from the prism is totally reflected by the multilayered structure and the reflectivity is equal to unity. Let us consider the case represented in fig. 2. The configuration involves four dielectric, homogeneous, isotropic, non absorbing media, two of which are thin films. The subscripts 1, 4 refer to the prism, gap, layer, resonant layer and the outside medium. The optical constants of the media (thickness dj, refractive index ni) are choosen as to give inhomogeneous fields in CZz and S& and homogeneous fields in C13. These conditions are easily obtained if the incidence angle 0 in the prism is smaller than the critical angle between !Cl, and .Q3 and larger than this one between a, and fi2, Qt. These conditions imply that the transmitted wave in !&t is evanescent and the field in a3 results from the superposition of two plane incident and reflected waves with amplitudes equal to A 3 and B3 respectively. It has been shown [ 121 that the field inside the resonant cavity is maximum, if the transverse resonance condition is satisfied by:
156
2Bd3 - $31 ~ +34 = 2mn,
(1)
where m is an integer which identifies the mode number. With k,, = w/c; B2 = kie3 - f12; G34 is the phase shift undergone by the incident wave A3 on the boundary Q31R,; $31 is the phase shift undergone by the B3 wave which is partially reflected on the C13/R,/a2, interface taking into account the presence of the prism. In this relation, /3 is the longitudinal propagation constant. The influence of the polarisa-
Volume 56, number 3
OPTICS COMMUNICATIONS
1 December 1985
tion TE or TM is involved through the phase shifts
A, B, C, are complex A’, A”, B’, B”, C’, C” are the
$31 and $34. For the TM case, tan $34 = e3C/qB and for d, > h = e3A/eZB, where and J/31= $32 with tan($32/2)
real and imaginary parts, respectively. When the metal film is thick enough. two surface plasma waves propagate on each surface of the film. If the thickness decreases the fields of these two surfaces waves overlap inside the metal layer and a long range and a short range plasma surface wave can be excited simultaneously with different propagation constants /3. The pairs of real and imaginary parts of fl are characteristic of the short range and long range surface plasma waves.
A2=fi2-k;e2,
C2=f12-k;e4.
(2)
The field in the resonant cavity is given by: U~(X, z) = exp(-jf3x)
[A3 exp(-jBz)
+B3exp(+jBz)]
, (3)
As, B3 are the amplitude
of the incident and reflected waves in a,. U3 = Ey in the TE case and U, = Hu in the TM case. The calculationofthe squared field U3 at the Q3/a4 interface normalised to the squared field U, in the prism is given by a=P[l-
Ir311 lr34lexp(-j 2Bd3 - G31 - J/34)1--2, (44 of the thickness d,,
where P is a quantity independent and r31 and r34 are the Fresnel reflection coefficients at the LI3/Q2,/Ql and !&/fi4 interfaces. As the transverse resonance condition is satisfied, the normalised field intensity is maximal and is given by s = B(1 - Ii-31 l)p
,
(4b)
where lr31 1is not equal to unity and depends on the thickness of the gap, and lr34 I = 1 as the a3 and s1, media are non absorbing. Due to the fact that lrN[ can be close to unity, the intensity can reach a high value. In the case oflong range plasmon polaritons, eqs. (1) can be used to give the dispersion relation of resonant TM modesguided by a thin metallic film surrounded by two adjacent dielectric media of almost equal refractive index. It has been shown [ 131 that a simplification of eq. (1) can be performed and provides the two following relations with real quantities: tan [(B’/B”) In lk I] + k”/k’ = 0 ,
(54
IklI2KB” ,
(5b)
d3 = -In
with k=(k34
-j)(Q-j)l(k34+j)(k32
k34 = tan(J/&),
k32 = tant$&)
+j), .
In eqs. (2), /3 is a complex variable: /3 = /3’ t j/I” where 0’ is related to the mode phase velocity and 0” is the mode attenuation coefficient. Only the mode m = 0 is considered. Note also that all the parameters
3. Results The following discussion is devoted to making a comparison of the field enhancements between the long range plasmas wave method and the resonant cavity excitation. We wish to show theoretically the magnitude of the field enhancements for both geometries discussed above. To demonstrate the field enhancement obtainable with both configurations (fig. 1, fig. 2), we choose parameters appropriate to the case of a silver metal film having dielectric constant e& = ~3 = -16 +j 0.52 at a wavelength of 632.8 nm bounded by two dielectric media of equal refractive index e2 = e4 = 2.25. For the resonant cavity configuration, we choose a high dielectric constant film a3 = 5.29 surrounded by the dielectric media e2 = e4 = 2.25. For both configurations, the incident light is coupled to the film through a high refractive index prism n 1 = 1.94325 or el = rzf = 3.78. The field enhancement can be only calculated with TM polarized light for the metal structure and with both TE and TM modes in the resonant dielectric structure. Fig. 3 shows the reflectivity curve as function of the incident angle inside the prism for dAg = 200 A and d,, = 9500 a and the angular width of the resonance close to 0.05”. The ratio u of the absolute square of the magnetic field inside the structure and the prism as function of z is shown in fig. 4 for three different incident angles: (a) 0 = 51.41” the resonant angle, (b) and (c) the angles corresponding to the half width of the resonance curve (fig. 3). The ratio is roughly divided by two. As the metal thickness decreases, the angular width of the resonance can be reduced by over an order of magni157
Volume
56. number
OPTICS COMMUNICATIONS
3
1 December
1985
‘base ;hift
0.
e 58. 91.30
51.40
SO
60.00
60. n1
91.50
Fig. 3. Reflectivity as a function of the incident angle 0 (degrees) for a long-range plasma wave geometry. The resonance angle occurs at 51.41” with eAg = -16 + j0.52, ~2 = ~4 = 2.25, E, = 3.78, and d& = 2008. Note the resonance width is close to 0.05”) corresponding to the 5 1.39” and 5 1.44” offresonance angles.
tude and the field enhancement can be higher. In this case, the system is limited by the diffraction effects associated with the finite width of the laser beam and by the angular aperture of the beam. These results have to be compared with the following curves in figs. 5,6,7,8. We calculated two config-
Fig. 5. Phase shift of the reflected beam as plotted as a function of the incidence angles e (degrees). The resonance angle occurs at 60” for TM polarized light with, er = 3.78, e2, ~4 = 2.25, es = 5.39, and d2 = 4000 A, d3 = 1095 A. The phase shift origin is arbitrary. The resonance width is close to 0.05“.
urations with the finite width of the laser beam and by the angular aperture of the beam. These results have to be compared with the following curves in figs. 5, 6, 7,8. We calculated two configurations with the dielectric resonant film; the first one is appropriate to the TM mode, (figs. 5,7), and the last to the TE mode (figs. 6,8). The thicknesses
lr
Phase shift
T-
a 0
100
200
e 76.
IO
76.20
3on
Fig. 4. Ratio o corresponding to the absolute square of the magnetic field IH~]~ inside the structure, divided by the incident magnetic field lHY I* in the prism as function of z. The curves given on the fire are calculated for the plasma resonance angles (a) and off-resonance (b and c). (a) 0 = 5 1.4 1”) (b) e = 51.39’;(c) e = 51.44”.
1.58
OI. IDO
Fig. 6. Phase shift of the reflected beam inside the prism as function of the incidence angle 0 (degrees). The resonance angle is at 76.12” for a TE polarized light. The gap and cavity thicknesses are respectively equal to 3000 A and 1095 A. The media are er = 3.78, ea = 2.25, es = 5.39, ~4 = 2.25. The phase shift origin is arbitrary. The resonance width is close to 0.05”.
OPTICS COMMUNICATIONS
Volume 56, number 3
0
400
BOO
1200
1 El00
Fig. 7. The ratio o (corresponding to the normalised IH,, 1’ for a TM polarized light) inside the resonant dielectric structure for the same parameters as given in fig. 5. The curves a, b, c, given on the figure are calculated for the incidence angles at resonance (60’) and off resonance (59.97” and 60.03”). The two curves corresponding to the off resonance angles are superposed.
of the gap layer and resonant cavity are equal to 4000 A and 1095 A for the TM mode; the maximum field enhancement occurs at the incidence angle of 60”. For the other confguration, the thicknesses are equal respectively to 3000 A and 1095 A for the TE mode.
1 December 1985
The maximum field enhancement is obtained for an incidence angle of 76” 12. In both cases, we considered only the m = 0 guided mode of the cavity. Around the resonance angle, the phase shift of the reflected beam undergoes a strong modification as shown in figs. 5,6. The slopes of the curves at 60’ and 76.12’ depend on the thickness of the gap. The angular resonance widths are evaluated from the linear part of the curve and are close to 0.05”. The choice of the gap thicknesses (3000 A and 4000 8, for TE and TM modes respectively) has been made to have the angular resonance width as in the case of the metal structure described above. Therefore, we can compare the field enhancements provided from these different configurations, with the same experimental conditions. Figs. 7 and 8 show the ratio u of the absolute squared IU12 inside the structure and in the prism versus z. We recall that U = HY (fig. 7) or U = Er (fig. 8) in TM or TE mode. If we compare the field enhancement, illustrated in fig. 4 for the metal film structure and fig. 7 for the resonant dielectric cavity. we note that the field intensity is roughly six times stronger in the dielectric structure as compared to the metal film (note the scale relative to the ratio u).
4. Conclusion We have compared the enhanced fields associated with the long range surface plasmon resonance and with the resonant cavity structure. We found that for the same angular width of the resonance, the dielectric structure can produce an enhancement six times higher than from the long range surface plasmons. Furthermore, the problem of dissipation of power in the metal which constitutes a thermal parasite effect can be avoided by the dielectric structure.
i0
0
Acknowledgement 1000
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Fig. 8. The ratio e (corresponding to the normalised @I” for a TE polarized light) inside the multilayered dielectric structure for the same parameters asgiven in fig. 6. The curves a, b, c, given on the figure are calculated for the incident angles at resonance (76.12’) and off resonance (76.09” and 76.14”).
The authors would like to thank J.D. Swalen from the IBM Research Laboratory, San Jose, California, for helpful discussions concerning the field enhancements.
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OPTICS COMMUNICATIONS
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[7] D. Sarid, Phys. Rev. Lett. 47 (1981) 1927. [ 81 R. Moshrefzadeh, R. Fortenberry, C. Karaguleff and G.I. Stegeman, N.E. Van Wijck, W.M. Hetherington III, Optics Comm. 46 (1983) 257. [9] R.T. Deck and D. Sarid, J. Opt.Soc.Am. 72(1982) 1613. [ 101 G.I. Stegeman, J J. Burke and D.G. Ha.& Appl. Phys. Lett. 41 (1982) 906. [ll] Y. Levy,Can. J.Phys. 58 (1980) 1525. [ 121 P.K. Tien and R. Ulrich, J. Opt. Sot. Am. 60 (1970) 1325. [ 131 D. Sarid, R.T. Deck and J J. Fasano, J. Opt. Sot. Am. 72(1982) 1345.